# Case and Commentaries

**Professional Knowledge**

**Practice Described:**

After teaching photography class to year seven students, I found myself explaining common photographic settings using fractions and ratios. With some research I adapted the next lesson to incorporate the teaching of photography using mathematics to a lower achieving school. The aperture of a lens is derived as the ratio between its focal length and the width of its aperture blades – also known as the iris – represented as f/2 (Focal length / aperture diameter width relative to the focal length). Additionally, the changes in aperture diameter can be seen and measured which not only piqued the interest of the students but is also gave the students an authentic learning experience. I demonstrated the aperture changes using the formulas on the board along with diagrams on the aperture opening to demonstrate why the images were getting brighter or darker. The increase from f/2 to f/4 gave half as much light; likewise, f/10 was a five times less than f/2. The students used this knowledge to make changes to their cameras settings. As a result the students were able to use mathematics in an authentic and engaged way and apply it to a photographic task. Furthermore, the shutter setting uses fractions of a second, and each adjustment made to the exposure adds or subtracts one third of a stop (A stop is a doubling or halving of light) giving plenty of room to discuss the use of fractions. The activity was successful, with the students enjoying the use of the camera.

# f/2

Focal length (f) = 50mm

50mm / 2 = 25mm

f/4

Focal length (f) = 50mm

50mm / 4 = 12.5mm

f/10

Focal length (f) = 50mm

50mm / 10 = 5mm

**Practice Explained:**

In order to implement the mathematics components within my lesson I worked in conjunction with the graduate teacher at KIOSC, who as mathematics specialist helped me to design the lesson. He suggested keeping it simple because students would be applying the knowledge to work out their problems rather than calculating them on paper. Additionally, I prepared extra questions that could be used during the lesson and studied up on my terminology. I targeted the goals of the lesson to the student’s achievement levels and in accordance with the Victorian Curriculum (2018). Through this discussion and using resources on camera mathematics (Martin 2004), I targeted the lesson at a standard that would cover both grade six and seven achievement levels (Victorian Curriculum 2018, VCMNA211; VCMNA212; VCMNA217; VCMNA243; VCMNA244).

**Practice Theorised:**

The exercise in operating a camera using fractions gave the students an opportunity to use both proper and improper fractions and commonly used together to achieve a goal. Student are required to interpret aperture using improper fractions such as ‘50/2’ (represented as f/2), and use it in conjunction with proper fractions such as those used in the cameras shutter which are all parts of a whole such as ‘½ sec’ to expose an image with the same quantity of available light. Booker (2014, pp. 157-158) states that ‘Fraction ideas also need to grow out of the use of materials that represent ones’, and this concept was utilised when using the shutter function of the camera representing fractions of a whole second. However, fractions are difficult for students to create mental images of (Austin 1981, p. 40), thus by using an authentic (Lombardi 2007) method such as the camera (AITSL 2018, 2.5), students can experience the changes in fractions through an outcome, a digital photograph (AITSL 2018, 2.6) which is either exposed correctly or not.

**Practice Changed:**

In future lessons focusing on one idea at a time would be far easier to implement while unfortunately taking more time. While mixing the two curriculum methods had many great advantages such as giving authentic outcomes using digital technologies, a number of students simply scrolled through the settings until the image exposed the way they desired or used the inbuilt light meter, with no thought of the fractions being used. However, the lesson was initially designed around photography and explaining some of the fractions will enable more students to understand how the camera works.

**References:**

Austin, K 1981, Teaching Fractions - Mathematics in School, *The Mathematics Association*, vol. 10, no. 5, p. 40.

Booker, G 2014, ‘Number and Algebra’, in *Teaching Primary Mathematics eBook, 5th edition*. Australia.

Lombardi, MM 2007, ‘Authentic Learning for the 21st Century: Overview’, *EDUCAUSE Learning Initiative*, viewed 26 March 2017, <https://library.educause.edu/resources/2007/1/authentic-learning-for-the-21st-century-an-overview>

Martin, MD 2004, *‘Photography and Math’*, Mr. Martin’s Web Site, viewed 5 October 2018, <http://www.mrmartinweb.com/photomath.html>

Victorian Curriculum 2018, *Mathematics*, Victorian Curriculum and Assessment Authority, viewed 10 October 2018, <http://victoriancurriculum.vcaa.vic.edu.au/mathematics/curriculum/f-10?y=6&y=7&s=NA&s=MG&s=SP&layout=2>

## Professional Practice

### Practice described:

During my second year placement at Gruyere Primary School it was critical that the teaching staff contributed to quality record keeping and monitoring, of which I also contributed. A running record for each student was kept detailing achievements, behaviour, relationships and more. As the school had only thirty students in total, many of the classes were taught as one big group, with students ranging from foundation to grade six. Additionally, the grade six students were achieving at a grade seven standard. As there was only one group the classes had to have a large amount of differentiation. However, with two full time teachers and a principal who also taught at least four days a week, it meant we could split the groups into three or four groups. Students were grouped based on their achievement and progress. Gruyere relied heavily on worksheets with their students as the large differentiation made it difficult to use hands on materials each time. Worksheets had positive outcome when it came to assessing the level that the students were achieving at. But it was also clear that the students were not as engaged as they were when they got the opportunity to use hands on materials. At the conclusion of the teaching day, teachers would ensure they saw each student picked up by their parent or guardians. During pickup time, it was common for teachers to have conversations with parents or guardians regarding their achievement (AITSL 2018, 3.7 & 5.5), which was important as students were not often categorised by their age group.

### Practice Explained:

In small primary schools the constant triage of dealing with the next most important item on the agenda is eased by good record keeping. Despite the students frequently using worksheets instead of hands on materials – a strategy that I would normally perceive as a disadvantage due to the disengaged environment typically created – the students were advantaged in other ways. For example, as all the students were in the same class, the younger students gained the advantage of many older more knowledgeable others (Vygotsky, cited in Nagel 2013, p. 81). Likewise the older students often assisted in teaching the younger students often solidifying their knowledge base in teaching to another (Frager & Stern 1970). Nevertheless, from the data we gathered through the worksheets we were able to differentiate learning programs for each of the students and convey the learning outcomes to parents, creating and engaging parent and guardian support in assisting student achievement.

**Practice Theorised:**

Freire’s (1970) ‘broad on build theory’ suggests that students need to engage with authentic situations (Lombardi 2007), instead of the ‘banking’ method in which students are delivered to in a one way learning environment. Worksheets have the risk of becoming a form of ‘banking’ methodology if incorrectly implemented. Gruyere understandably used worksheets to differentiate and assess a wide diversity of students. However, instead of implementing worksheets, there are other strategies that could be adopted such as inquiry learning in which assessments should ‘make students’ thinking visible to teachers and themselves’ (Fergusson 2013, p. 426; Moss et al. 2006, p. 17). Furthermore, integrated home work can then be viewed by parents who can themselves gauge their child’s progress. Parental involvement is critical in student outcomes) so teachers need to create opportunities for parents to receive professional feedback on their students learning both formally and informally and enable parents to be able to use that feedback to enable them to assist in their child’s achievement (Minke et al. 2014, p. 527).

### Practice Changed:

In an ideal classroom there would be plenty of hands on activities with formative assessments built in so students can be assessed while they learn. In practice this is not always possible, and reporting results to parents is a critical component, thus the use of worksheets in this scenario is justified. One solution is using newer ICT programs such as Literacy Planet which allow students to continue at their own pace, with inbuilt tools for teachers to use for assessment. Parents can also monitor their children as they can work from home as much or as little as they like. However, students would then miss out on learning tasks such as handwriting.

### References:

Frager, S & Stern, C 1970, Learning by Teaching, *The Reading Teacher, *vol. 23, no. 5, pp. 403-405, 417.

Fergusson, P 2013, ‘Assessment, Feedback and Reporting’, in Churchill, R, Ferguson, P, Godinho, S, Johnson, N, Keddie, A, Letts, W, Mackay, J, McGill, M, Moss, J, Nagel, M, Nicholson, P, Vick, M 2013, *Teaching: Making a Difference, *2nd Edition, John Wiley & Sons, Milton, QLD, pp. 412-458.

Literacy Planet 2018, Primary, Intrepica Pty Ltd, Viewed on 14 October 2018, <https://www.literacyplanet.com/au/>

Lombardi, MM 2007, ‘Authentic Learning for the 21st Century: Overview’, *EDUCAUSE Learning Initiative*, viewed 26 March 2017, <https://library.educause.edu/resources/2007/1/authentic-learning-for-the-21st-century-an-overview>

Minke, KM, Sheridan, SM, Kim, EM, Ryoo, JH & Koziol, NA 2014, Congruence in Parent-Teacher Relationships The role of Shared Perceptions, *The Elementary School Journal,* vol. 114, no. 4, June, pp. 527-546.

Moss, PA, Girard, BJ, Haniford, LC 2006, ‘Validity in Educational Assessment’ in *Review of Research In Education, *vol. 30, Special Issue on Rethinking Learning: What Counts as Learning and What Learning Counts, pp. 109-162.

Nagel, M 2013, *‘*Student learning’, in Churchill, R, Ferguson, P, Godinho, S, Johnson, N, Keddie, A, Letts, W, Mackay, J, McGill, M, Moss, J, Nagel, M, Nicholson, P, Vick, M 2013, *Teaching: Making a Difference, *2nd Edition, John Wiley & Sons, Milton, QLD, pp. 74-111.

## Professional Engagement

### Practice Described:

For the past two years I have been delivering professional development (PD) to schools in the area of advanced manufacturing and computer aided design (CAD). During my final year I had the opportunity to deliver a session to a previous placement school at Mt Lilydale Mercy College at the request of the head of Arts, as their Visual Communications and Design teacher was on leave for the remainder of the year (AITSL 2018, 6.1, 6.2 & 7.4). The focus of the PD session was to introduce the arts staff to using Autodesk Fusion 360 a CAD program which would be used to design and created prototypes using the newly purchased 3D printer. The PD was delivered in two after school sessions running for a total of three hours. The PD was designed to enable teachers to teach student CAD and product prototyping, as such the session included content which focused on the VCE curriculum (AITSL 2018, 6.1, 6.2 & 6.4; VCE 2018, Unit 2, Study Area 1). The teachers then 3d printed their PD work projects, experimented with them, and redesigned them – completing the design process (Illinois CITL 2018).

### Practice Explained:

The PD concentrated on delivering skills and knowledge to teachers so that they could stand in while the usual teacher was on leave; therefor it was critical that the session reflected the curriculum (VCE 2018) and skills required by students (AITSL 2018, 6.1, 6.2 & 6.4). As the school had purchased a 3D printer, I had designed the content in order to utilise it. The additional of having a hands on machine producing items that teachers and students can see, touch and respond to bridges a divide between ICT and real world authentic learning scenarios. Having attended, delivered, and studied education, I have a strong understanding the needs of both teachers and students learning, and how to deliver the content in an effective manner.

### Practice Theorised:

The purpose of professional development is to improve the teaching practice and to inform of the changes to the profession. It was entirely possible for staff at Mt Lilydale Mercy College to teach their Visual Communications classes. However, with a fresh perspective the classes taught will ideally ‘benefit from a re-evaluation’ (Howard 1996, p. 60), and this is achieved by introducing new ideas and pedagogies, which results in teaching current educational models, techniques and content knowledge. Additionally it is critical that school communities meet regularly to ‘discuss evidence, to analyse that evidence, question it and interpret it as a community of practice’ (Ewing, Groundwater-Smith, Le Cornu 2015, p. 354). In this meeting, student needs, the syllabus and pedagogical focus can be established, allowing for professional development to occur (AITSL 2018, 6.1, 6.2, 6.4 & 7.4).

### Practice Changed:

In delivering professional development, I am given a unique perspective as a student teacher to improve my own learning when I undertake professional development. I understand that there is always another perspective, skill, pedagogy or attribute that I can bring to my own teaching practice.

**Click and drag the model below to view the PD object created from multiple angles. Use scroll to zoom in and out and right click to drag.**

### References:

Ewing, R, Groundwater-Smith, S, Le Cornu, R 2015, ‘The effective Teacher’ in *Teaching Challenges & Dilemmas*, 5th edition, Cengage Learning Australia, South Melbourne, pp. 353-359.

Howard, CD 1996, Professional Development, * The Science Teacher,* vol. 63, no. 8, pp. 60, 62-65.

Illinois CITL 2018, *Design Thinking*, Illanois Center for Innovation in Teaching and Learning, viewed on 14 October 2018, <http://citl.illinois.edu/paradigms/design-thinking>

Victorian Certificate of Education 2018, *Visual Communication Design*, Victorian Curriculum and Assessment Authority, viewed on 14 October 2018, <https://www.vcaa.vic.edu.au/Documents/vce/visualcomm/VisualCommunicationDesignSD_2018.pdf>